Find Relative Error of A: 2.33

[evinda]

Hey! I have also an other question
Suppose the base $\beta =10$ ,the precision $t=3$, $-L=U=10$ and $$A=(317+0.3)-(171.499+145.501)$$
I have to find the relative error for $A$.
We don't make rounding.For example,if we have the value $345.924$ it is equal to $0.345924*10^3$ and the corresponding floating number is $0.345*10^3$.
I found that it is equal to
$$\frac{||A-fl(A)||}{||A||}=\frac{7}{5}=2.33$$
Could you tell me if it is right?

 

[evinda]

Hey! I have also an other question
Suppose the base $\beta =10$ ,the precision $t=3$, $-L=U=10$ and $$A=(317+0.3)-(171.499+145.501)$$
I have to find the relative error for $A$.
We don't make rounding.For example,if we have the value $345.924$ it is equal to $0.345924*10^3$ and the corresponding floating number is $0.345*10^3$.
I found that it is equal to
$$\frac{||A-fl(A)||}{||A||}=\frac{7}{5}=2.33$$
Could you tell me if it is right?

I found that A=0.3 and fl(A)=1..

 

[I like Serena]

I found that A=0.3 and fl(A)=1..

Looks good! ;)... but doesn't that mean that:
$$\frac{||A-fl(A)||}{||A||} = \frac{|0.3 - 1|}{|0.3|} = \frac{0.7}{0.3} = 2.33$$

Oh wait! You also got $2.33$... while you shouldn't have.

 

[evinda]

Looks good! ;)... but doesn't that mean that:
$$\frac{||A-fl(A)||}{||A||} = \frac{|0.3 - 1|}{|0.3|} = \frac{0.7}{0.3} = 2.33$$

Oh wait! You also got $2.33$... while you shouldn't have.

I accidentally wrote $\frac{7}{5}$ I meant that it is equal to $\frac{7}{3}$..

Thank you very much! (Mmm)

 

[CellCoree]

Yes, your calculation for the relative error of A is correct. The relative error is a measure of how much the calculated value of A differs from the actual value, expressed as a percentage. In this case, the relative error is 2.33 or 233%. This indicates that the calculated value of A is 233% off from the actual value. It is important to minimize the relative error in scientific calculations, as it can affect the accuracy and reliability of the results.